My stepdad is a veteran with Alzheimer's, will my Mom lose his income if he's put into a nursing home?

Here is a document from the VA about survivor benefits with contact information at the end. Good luck in getting the answers you need.

http://benefits.va.gov/BENEFITS/benefits-summary/SummaryofVADependentsandSurvivorsBenefits.pdf

go to the box above "money and legal" and click on "veterans assistance". The VA takes care of their own.

Depends on what type of income he has.